Question

Find the domain of the following function:

`f(x)sin^-1sqrt(x^2-1)`

Answer 1

To the domain of sin^-1 y which is [−1, 1] 

∴ x² - 1 ∈ [0, 1] as square root can not be negative

⇒ x² ∈ [0, 1]

⇒ x ∈ [−√2, −1] ∪ [1, √2]

Hence, the domain is [- √2, -1] ∪ [1, √2]